Checking if a vertex belongs to a vertex group in python
What you basically want is something like this:

import bpy
ob = bpy.data.objects["Cube"]
gi = ob.vertex_groups["Group"].index # get group index
for v in ob.data.vertices:
  for g in v.groups:
    if g.group == gi: # compare with index in VertexGroupElement
      v.co[0] = 5


v.groups is a collection of VertexGroupElements. VertexGroupElement contains group (as index) and weight (as float [0,1]).

find can not find anything, because v.groups does not contain any keys.